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Articles 1 - 6 of 6
Full-Text Articles in Logic and Foundations of Mathematics
The Logic Of Concessive Statements, Aharon Grenadir
The Logic Of Concessive Statements, Aharon Grenadir
School for Lifelong Education Publications
Concessive statements appear frequently in everyday reasoning. They are one of the eleven types of statement mentioned in the Ramchal‟s Sefer Derech Tevunos. In addition, in Talmudic discussions, every statement has a presupposition (hava-amina) and a conclusion (ka mashma lan). This goal of this research is to organize the categorizations of concessive statements that are stated in the technical literature. Using the distintinction in lomdus between dechiyah (overriding a law) and hutrah (removal of a law), a novel categorization can be added, according to the type of denial of the expectation by the main clause. That is the subject of …
Abstraction And Epistemic Economy, Marco Panza
Abstraction And Epistemic Economy, Marco Panza
MPP Published Research
Most of the arguments usually appealed to in order to support the view that some abstraction principles are analytic depend on ascribing to them some sort of existential parsimony or ontological neutrality, whereas the opposite arguments, aiming to deny this view, contend this ascription. As a result, other virtues that these principles might have are often overlooked. Among them, there is an epistemic virtue which I take these principles to have, when regarded in the appropriate settings, and which I suggest to call ‘epistemic economy’. My purpose is to isolate and clarify this notion by appealing to some examples concerning …
What Do We Mean By Logical Consequence?, Jesse Endo Jenks
What Do We Mean By Logical Consequence?, Jesse Endo Jenks
Summer Research
In the beginning of the 20th century, many prominent logicians and mathematicians, such as Frege, Russell, Hilbert, and many others, felt that mathematics needed a very rigorous foundation in logic. Many results of the time were motivated by questions about logical truth and logical consequence. The standard approach in the early part of the 20th century was to use a syntactic or proof-theoretic definition of logical consequence. This says that "for one sentence to be a logical consequence of [a set of premises] is simply for that sentence to be derivable from [them] by means of some standard system of …
Ante Rem Structuralism And The No-Naming Constraint, Teresa Kouri
Ante Rem Structuralism And The No-Naming Constraint, Teresa Kouri
Philosophy Faculty Publications
Tim Räz has presented what he takes to be a new objection to Stewart Shapiro's ante rem structuralism (ARS). Räz claims that ARS conflicts with mathematical practice. I will explain why this is similar to an old problem, posed originally by John Burgess in 1999 and Jukka Keränen in 2001, and show that Shapiro can use the solution to the original problem in Räz's case. Additionally, I will suggest that Räz's proposed treatment of the situation does not provide an argument for the in re over the ante rem approach.
Restall's Proof-Theoretic Pluralism And Relevance Logic, Teresa Kouri
Restall's Proof-Theoretic Pluralism And Relevance Logic, Teresa Kouri
Philosophy Faculty Publications
Restall (Erkenntnis 79(2):279–291, 2014) proposes a new, proof-theoretic, logical pluralism. This is in contrast to the model-theoretic pluralism he and Beall proposed in Beall and Restall (Aust J Philos 78(4):475–493, 2000) and in Beall and Restall (Logical pluralism, Oxford University Press, Oxford, 2006). What I will show is that Restall has not described the conditions on being admissible to the proof-theoretic logical pluralism in such a way that relevance logic is one of the admissible logics. Though relevance logic is not hard to add formally, one critical component of Restall’s pluralism is that the relevance logic that gets added must …
A New Interpretation Of Carnap's Logical Pluralism, Teresa Kouri
A New Interpretation Of Carnap's Logical Pluralism, Teresa Kouri
Philosophy Faculty Publications
Rudolf Carnap’s logical pluralism is often held to be one in which corresponding connectives in different logics have different meanings. This paper presents an alternative view of Carnap’s position, in which connectives can and do share their meaning in some (though not all) contexts. This re-interpretation depends crucially on extending Carnap’s linguistic framework system to include meta-linguistic frameworks, those frameworks which we use to talk about linguistic frameworks. I provide an example that shows how this is possible, and give some textual evidence that Carnap would agree with this interpretation. Additionally, I show how this interpretation puts the Carnapian position …